Author:
Mark Freed, Tom Thompson
Subject:
Mathematics
Material Type:
Homework/Assignment
Level:
Middle School
Tags:
Applied Mathematics, Oregon Math in Real Life, STEM Education
License:
Creative Commons Attribution Non-Commercial
Language:
English

Education Standards (14)

Electric Motorcycle Race

Electric Motorcycle Race

Overview

Math in Real Life (MiRL) supports the expansion of regional networks to create an environment of innovation in math teaching and learning.  The focus on applied mathematics supports the natural interconnectedness of math to other disciplines while infusing relevance for students.  MiRL supports a limited number of networked math learning communities that focus on developing and testing applied problems in mathematics.  The networks help math teachers refine innovative teaching strategies with the guidance of regional partners and the Oregon Department of Education.

Lesson Overview

Introduction

Students need to decide how fast they will ride and where they will need to charge their electric motorcycle in order to make it from Ashland, OR to Blaine, WA in the least time possible. What is the optimal speed to minimize travel time between Ashland, OR and Blaine, WA?

Students will figure out how far their motorcycle can drive using unit rates and unit conversions to determine how far they can drive at each speed before running out of power.

Background for Teachers

Brammo Inc. was a leading electric vehicle technology company headquartered in North America. Brammo designed, developed and integrated electric powertrains. Since this lesson was developed , Brammo production has been discontinued.

Videos

Core Math Concepts

  • Understand what a unit rate means and use it to make decisions.
  • Secondary goal: Reason mathematically using rational numbers.

Student Objectives

  • I can use unit rates and conversions to determine how many miles I can drive before running out of power at various speeds.
  • I can compute with rational numbers.

Materials

  • Maps of Oregon/Washington (1 per group or student)
  • Student worksheet (1 per student)
  • Student Info Sheet (1 per student)
  • Calculators (1 per student)

Time Required

Two or three 45-minute lessons (one or two 90-minute lessons)

Authors

Jamar Boyd, Heather Armstrong, Peg Hansen, and Gordon Sievers. Special thanks to: Joe Keto

Standards

7.RP.1     Compute unit rates associated with ratios of fractions, including ratios of lengths, area, and other quantities measured in like or different units.

7.NS.3    Solve real world problems with rational numbers.

7.EE.3     Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies.

6.RP.3     Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Practice Standards

4.       Model with mathematics

5.       Attend to precision.

6.       Use appropriate tools strategically.

1.       Make sense of problems and persevere in solving them.

Key Words

Speed, wattage (Watts), amperage (amps), voltage (volts), electric, charge, mph, kWh, kW, miles, distance, batteries

LAUNCH - SET UP

Anticipated Time:

20 Minutes

Suggested Grouping:

Individual/Pairs, Class Discussion

Teacher Questions and Actions: 

Show a video of motorcycle race and Brammo showing off bike technology to introduce the idea of the electric motorcycle rally.

Monitor students’ private reasoning time to generate at least two questions on their own. Allow groups 3 minutes to share questions. Make a public record of student questions.

Explain the specifications of the motorcycle.

  • The bike can go up to 100 mph. (It’s gone over a hundred on a race track.)
  • The battery holds 10.4 kWh
  • The speed limit is 65 mph on most stretches of I-5 in Oregon. The speed limit is 70 mph for
  • most of I-5 in Washington. It drops down to 55 mph while passing through cities and highly populated areas. Note: kids get to decide if they want to follow the speed limit or not.
  • There are several types of charging stations.
  • See info sheet for details.

Tell the students that certain factors were left out in order to simplify the problem for middle school level math including:

Traffic, terrain, weight of motorcycle and rider, uphill/downhill/curves, weather, position of rider (prone or upright).

If they ask questions about these, acknowledge that these are valid questions and would absolutely affect how fast/far the bike could travel, but that we won’t be looking at those factors today.

Student Moves: 

Have students come up with a list of questions of what they would need to know before planning a route for their bike race.

List of possible student questions (* are questions that you want to come out.):

  • How fast does the motorcycle go?
  • How far can it go before it runs out of power?
  • How long does it take to charge it?
  • Where can it be charged? How does it get charged?
  • What’s the speed limit? Do you have to drive the speed limit?
  • How many hours can you drive in one day?
  • How far is it from Ashland to Blaine? What time will we leave?
  • How much traffic is there?
  • What’s the average driving time from Ashland to Blaine?
  • What kind of terrain/wheels/traction etc? Will weather affect driving?
  • Does the battery drain faster going uphill, downhill, same?

Warm Up (Teacher Notes)

Give students the maps of Oregon and Washington and the Student Info Sheet

For Questions #1 and #2:

  • Allow students a couple minutes of private reasoning time before sharing ideas in groups.
  • Have a student present their idea to the class to make sure everyone knows how to find the difference between two places using the mile markers. You may need to talk about what the mile markers mean.

Revisit this idea within Question #3 during your summary, but for now just let a couple ideas percolate in class.

Warm Up Questions (Student)

  1. What is the total distance from Ashland, OR to Blaine, WA?

Correct Answer:

308 − 14 = 294 miles in Oregon

276 − 0 = 276 miles in Washington

Total miles 294 + 276 = 570 miles

Misconceptions

276 + 14 = 290 (adding Ashland’s and Blaine’s mile markers)

308 − 14 = 294 miles in Oregon

276 − 5 = 271 miles in Washington

  1. Traveling at 60 miles per hour, how long would it take you to travel from Ashland to Blaine?

Correct Answer:

570 miles divided by 60 miles per hour equals 9.5 hours.

  1. I think I will be able to go the farthest driving ____ mph because….

Possible student answers:

“I think I will be able to go the farthest driving 40 mph because the table shows you can drive more miles going slower.”

“I think…. 100 mph because that’s the fastest it can go.”

“I think … 40 mph because going slower takes less energy.”

EXPLORE - INVESTIGATE

Anticipated Time:

40-50 minutes -break into 2 days as needed

Suggested Grouping:

Groups of 4 and Class Discussion

Discussion 1:

Teacher Questions or Actions 

Introduce the different types of charging stations available and explain watts.

For a 10.4 kWh battery:

  • Level 2: takes 2.95 hours for full charge
  • Fast Charge: takes 0.98 hours for a full charge

What is a Watt? (1.5 minutes)

What is a Kilowatt Hour (kWh)? (1 minute)

Student Moves or Actions

What the student needs to know from videos:

  • Watts are the units used to measure power. (Both the power going out of the motorcycle when riding and the power going into the battery while charging.)

A kilowatt hour is a way to measure the amount of power used in an hour.

Discussion 2:

Teacher Questions or Actions 

Prompt Students to fill in the table:

  • What is the maximum number of hours/distance that you can ride at each speed?
  • Choose 3 more speeds and then fill in the table. Show your math reasoning for at least two of the speeds.

Suggested Actions:

  • During the check in with the groups (or a class huddle), clarify that students will need units to match before completing their calculations.
  • Encourage groups to convert to kW.

Sharing Thinking:

  • Choose a student to present their groups’ strategies. Make a public record so students who are struggling can refer to the idea as they repeat the process for each of the other speeds.

Student Moves or Actions

First students need to determine how many kilowatts are used at each speed by looking at the watts on the table and converting to kilowatts.

At 60 mph, the bike uses 4,700 watts or 4.7 kW (divide by 1000).

Students should calculate that they have 10.4 Kilowatt-hours divided by the average number of Kilowatts (4.7) equals the number of hours before running out of power.

10.4 kilowatt hours divided by 4.7 kilowatts equals 2.21 hours

60 mph × 2.21 hours = 132.6 miles

Misconceptions or Sticking Points:

  • Some students will not remember or know how to convert watts to kilowatts and vice versa.
  • Some groups may not know how to determine how many hours the battery can run with 10.4kWh available.

Discussion 3:

Teacher Questions or Actions 

After most groups have finished all 5 speeds they chose, fill in the table on the Student Info Sheet together.

This is time consuming for students to complete all 13 speeds on their own. You also want to make sure they have all the correct info.

Student Moves or Actions

Students copy the table on the student info sheet.

Discussion 4:

Teacher Questions or Actions 

Plan at least 2 different routes to determine the least time it will take you to drive from Ashland, OR to Blaine, WA. Think about how you want to organize and display your routes.

Teacher move: allow a student to present part of a route that wouldn’t work. Prompt students to decide that it’s impossible if they don’t do it on their own.

Student Moves or Actions

Students should begin planning their routes with their group. (If you are splitting this lesson into two days, this would be a good homework assignment). The following day, students could compare their routes and decide whose is fastest.

Misconception:

Some students may try to drive farther than the battery would allow. In other words, they may decide to drive from Ashland to Eugene at 100 mph.

SUMMARIZE - CLOSE

Anticipated Time:

10-15 minutes

Suggested Grouping:

Class Discussion

Teacher Summary:

Allow groups to check each other’s routes and discuss why certain routes were shorter than others. (They want to figure out what is the fastest they can drive and still make it to a Fast-Charge station.)

Possible Questions:

  • How does your speed affect your travel time?
  • How does your final route compare to your conjecture?
  • What might you do different next time?
  • How could you cut time off of the travel time?
  • Compare each of these student approaches. Which approach seems to be the most efficient?

Misconception:

Students may try to convert 13.39 hours into 13 hours and 39 minutes.

Anticipated Responses:

Students copy the table on the student info sheet.

Speed (mph)

City to City

Miles Driven

Drive Time (hrs)

Charge Time (hrs)

Total Time (hrs)

60

Ashland to Roseburg

109

1.81

2.95

4.76

60

Roseburg

to Albany

111

1.85

2.95

4.80

60

Albany to Castle R.

128

2.10

2.95

5.00

60

Castle R. to Seattle

116

1.90

0.98

2.88

60

Seattle to Blaine

111

1.85

0.00

1.85

Total

 

 

 

 

19.29

 

 

Speed (mph)

City to City

Miles Driven

Drive Time (hrs)

Charge Time (hrs)

Total Time (hrs)

45

Ashland to Eugene

185

4.10

0.98

5.08

65

Eugene to Vancouver

114

1.75

0.98

2.73

55

Vancouver to Seattle

160

2.90

0.98

3.88

65

Seattle to

Blaine

111

1.70

0.00

1.70

Total

 

 

 

 

13.40

 

Speed (mph)

City to City

Miles Driven

Drive Time (hrs)

Charge Time (hrs)

Total Time (hrs)

100

Ashland to GP

44

0.44

2.95

3.39

90

GP to Roseburg

65

0.72

2.95

3.67

85

Roseburg to Eugene

76

0.89

.98

1.87

100

Eugene to Salem

57

0.57

2.95

3.52

100

Salem to Portland

48

0.48

0.98

1.46

100

Portland to Castle Rock

53

0.53

2.95

3.48

100

Castle Rock to Olympia

56

0.56

2.95

3.51

95

Olympia to Seattle

60

0.63

0.98

1.61

100

Seattle to Mt. Vernon

60

0.60

2.95

3.55

100

Mt. Vernon to Blaine

51

0.51

Done!

0.51

Total

 

 

 

 

26.57

 

Exit Task:

If you drove 55 mph, how long would it take you to get from Salem to Castle Rock?

Extensions:

Introduce limits to the context such as speed limits, rush hour traffic restraints, or a different destination or motorcycle with a different battery capacity.

Notes/Reflections/Suggestions:

Many students wanted to figure out partial charges. Though scientifically it doesn’t work out to be a straight proportion, it would be a great chance to bring in some proportions. Not all students need to go there, but if a student wants to set up a proportion to figure out how long it would take to charge a partially charged battery, allow it and have them share their idea with the class.

You may want to spend time converting hours from decimal form into hours and minutes.

References: